Visiting United held a 3-1 advantage in the 57th minute courtesy of a flicked effort from Ander Herrera, but in the minutes that remained, hosting Leicester hit four unanswered goals to secure all three points.
Writing about the performance on his official blog, Mata, who came on as a substitute at the King Power Stadium, said: "I have waited a few hours before facing the white screen to try to express how I feel after the game in Leicester. After a whole week waiting for the match I could not imagine a Sunday like this. The way back from Leicester to Manchester on the bus seemed really long.
"I keep thinking about how we lost a game that was under control, but the thing is we were ahead, they equalised and when we tried to get advantage again we lost. It's really tough to score three goals away and come back home with no points.
"On our way back to Manchester I was thinking about what had happened and felt so disappointed as all those that came with us to the stadium. Honestly, I feel very sorry that the weekend ended up for our fans in such a sad way."
Next up for the Red Devils is back to back home encounters against West Ham United and Everton and Mata has insisted that the players will be putting in their "best efforts" to win those two games.
"There is time during the week to analyse what happened and learn from our mistakes so as not to make them again. Now we play two consecutive games in Old Trafford that we want to win for our fans. We will put our best efforts to it, you can be sure of that," the Spaniard added.
"I hope to be in a better mood next Sunday to tell you about the game and many other things, to try to put a smile in our face on Monday."